結果

問題 No.824 Many Shifts Hard
コンテスト
ユーザー maroon_kuri
提出日時 2019-04-27 00:00:48
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 129 ms / 2,000 ms
コード長 6,024 bytes
コンパイル時間 1,542 ms
コンパイル使用メモリ 172,924 KB
実行使用メモリ 53,828 KB
最終ジャッジ日時 2024-11-25 08:32:11
合計ジャッジ時間 4,193 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
other AC * 23
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
#include <type_traits>
using namespace std;

using ll=long long;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) FOR(i,0,b)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define REACH cerr<<"reached"<<endl
#define DMP(x) cerr<<#x<<":"<<x<<endl
#define ZERO(x) memset(x,0,sizeof(x))
#define ONE(x) memset(x,-1,sizeof(x))

template<class T> using V=vector<T>;
template<class T> using VV=V<V<T>>;

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	rep(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"(";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<")";
}

ll read(){
	ll i;
	scanf("%lld",&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%lld",x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

constexpr ll TEN(int n){
	return n==0?1:TEN(n-1)*10;
}

template<class T>
vector<T> Uniqued(const vector<T>&vv){
	auto v(vv);
	sort(all(v));
	v.erase(unique(all(v)),v.end());
	return v;
}
template<class T>
void MakeUniqued(vector<T>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.end());
}

template<int mod>
struct ModInt{
	static constexpr int base=mod;
	int v;
	ModInt():v(0){}
	ModInt(ll vv){
		v=vv%mod;
		if(v<0)v+=mod;
	}
	explicit operator bool()const{
		return v;
	}
	explicit operator int()const{
		return v;
	}
	bool operator==(const ModInt&rhs)const{
		return v==rhs.v;
	}
	bool operator!=(const ModInt&rhs)const{
		return v!=rhs.v;
	}
	ModInt operator-()const{
		return ModInt(0)-*this;
	}
	ModInt& operator+=(const ModInt&rhs){
		v+=rhs.v;
		if(v>=mod)v-=mod;
		return *this;
	}
	ModInt&operator-=(const ModInt&rhs){
		v-=rhs.v;
		if(v<0)v+=mod;
		return *this;
	}
	ModInt&operator*=(const ModInt&rhs){
		v=ll(v)*rhs.v%mod;
		return *this;
	}
	ModInt&operator/=(const ModInt&rhs){
		operator*=(rhs.inv());
		return *this;
	}
	ModInt operator+(const ModInt&rhs)const{
		return ModInt(*this)+=rhs;
	}
	ModInt operator-(const ModInt&rhs)const{
		return ModInt(*this)-=rhs;
	}
	ModInt operator*(const ModInt&rhs)const{
		return ModInt(*this)*=rhs;
	}
	ModInt operator/(const ModInt&rhs)const{
		return ModInt(*this)/=rhs;
	}
	friend ModInt operator+(int x,const ModInt&y){
		return ModInt(x)+y;
	}
	friend ModInt operator-(int x,const ModInt&y){
		return ModInt(x)-y;
	}
	friend ModInt operator*(int x,const ModInt&y){
		return ModInt(x)*y;
	}
	friend ModInt operator/(int x,const ModInt&y){
		return ModInt(x)/y;
	}
	ModInt pow(int n)const{
		ModInt res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	ModInt inv()const{
		return pow(mod-2);
	}
};

template<int mod>
ostream& operator<<(ostream&os,const ModInt<mod>&m){
	return os<<m.v;
}
template<int mod>
void print(const ModInt<mod>&m,int suc=1){
	print(m.v,suc);
}

using mint=ModInt<1000000007>;
//using mint=ModInt<998244353>;

const int Vmax=min<int>(2000010,mint::base);
mint fact[Vmax],factInv[Vmax],invs[Vmax];
void InitFact(){
	fact[0]=1;
	FOR(i,1,Vmax){
		fact[i]=fact[i-1]*i;
	}
	factInv[Vmax-1]=fact[Vmax-1].inv();
	for(int i=Vmax-2;i>=0;i--){
		factInv[i]=factInv[i+1]*(i+1);
	}
	for(int i=Vmax-1;i>=1;i--){
		invs[i]=factInv[i]*fact[i-1];
	}
}
struct InitFactDummy{
	InitFactDummy(){
		InitFact();
	}
} initFactDummy;
mint Choose(int n,int k){
	return fact[n]*factInv[n-k]*factInv[k];
}
mint Binom(int a,int b){
	return fact[a+b]*factInv[a]*factInv[b];
}
mint Catalan(int n){
	return Binom(n,n)-(n-1>=0?Binom(n-1,n+1):0);
}

const int Kmax=310;
mint dp[2][Kmax][Kmax];

signed main(){
	int n=read(),k=read();
	if(n==1){
		print(0);
		return 0;
	}
	int cur=0;
	FOR(i,1,n+1){
		int j=min(n-i,Kmax-5);
		dp[cur][j][j+1]+=i;
	}
	const mint in=mint(n).inv();
	rep(_,k){
		int nx=cur^1;
		ZERO(dp[nx]);
		rep(i,Kmax)FOR(j,i+1,Kmax){
			auto w=dp[cur][i][j]*in;
			dp[nx][i][j-1]+=w;
			if(i==0){
				dp[nx][i][j]+=w*(n-1);
			}else{
				dp[nx][i][j]+=w*(n-2);
				dp[nx][i-1][j]+=w;
			}
		}
		cur=nx;
	}
	mint ans=0;
	rep(i,Kmax)FOR(j,i+1,Kmax)
		ans+=dp[cur][i][j];
	ans*=mint(n).pow(k);
	print(ans);
}
0